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Chapter 9: Q. 23 (page 721)

In Exercises 16鈥�23 sketch the parametric curve by plotting points.

23.x=cos5t,y=sin5t,t鈭�[0,2蟺]

Short Answer

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We've plotted the required graph

Step by step solution

01

Given information

Given :x=cos5t,y=sin5t,t鈭�[0,2蟺]

02

:Substituting different values in the parametric equations 

Find the values of x,yby substituting different values in the parametric equations :

(a) When t=0, the point (x,y)is :

(x,y)=(sin5t,cos5t)=(sin50,cos50)...(sincet=0)=(0,1)

(b) When t=蟺(x,y)is :

(x,y)=(sin5t,cos5t)=(sin5蟺,cos5蟺)...[byinsertingt=蟺],=(0,-1)

03

:Substituting different values in the parametric equations

(c) When t=3蟺2,(x,y)is :

(x,y)=(sin5t,cos5t)=(sin53蟺2,cos53蟺2)...(sincet=3蟺2)=(-1,0)

04

Plotting graph

The required graph is :

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